In the analysis of Ref. [1]}, a flat prior was assumed on the component masses and deviation parameter \(\delta \hat{\varphi }_{-2}\) .
(We note that the upper prior bound is dictated by the theory since \(\delta \hat{\varphi }_{-2} \le 0\) , see Eq. (REF ).)
These choices reflect the theory-agnostic nature of that test; without a preferred alternative, this choice represents the simplest prior in terms of these binary parameters. Figure REF  depicts with dashed lines how this choice of prior distribution maps to an assumed prior on \(\alpha _0\)  through Eq. (REF ); here the different colors correspond to different assumed EOSs.
Similarly, the dashed lines in Fig. REF  show the corresponding marginalized posteriors on \(\alpha _0\) , transformed from the posterior on \(\delta \hat{\varphi }_{-2}\)  and component masses via Eq. (REF ).
This analysis provides a bound of \(\alpha _0 \lesssim 2\times 10^{-1}\)  (\( 5\times 10^{-1}\) ) at a 68% (90%) credible level. We find that that the systematic error arising from our ignorance of the NS EOS does not impact our estimate at 68%, but change the bound at 90% CL by \(\sim 30\%\) . The bound on \(\alpha _0\)  with GW170817 is about three orders of magnitude larger than what
obtained with the double-pulsar J0737-3039 [2]},
which since 2003 has been tracked for about 60 000 orbital cycles. Future observations with GW detectors on the ground and in space, will allow to reach similar or better accuracies [3]}. Due to the much smaller velocity (\(v/c \sim 2 \times 10^{-3}\) ), the double-pulsar observation becomes quickly less constraining for high PN terms entering the GW phasing (i.e., the ones discussed in Sec. ).
